Speaker: Cheryl Praeger (Perth)
Title: Complexity of Bray's Involution Centraliser Algorithm for Classical Groups in Odd Characteristic
Bray's involution centraliser algorithm plays a key role in recognition algorithms for classical groups over finite fields of odd order. It has always performed faster than the time guaranteed/justified by complexity analyses. Work of Dixon, Seress and I published this year give a satisfactory analysis for SL(n,q). And we are slowly making progress with the other classical groups. The "we" are Colva Roney-Dougal, Stephen Glasby and me - and we have conquered the unitary groups so far.